The microstructural, spectral, magnetic and electric properties of hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ (0.00 ¡Â x ¡Â 0.30) synthesized by the solid-state reaction route have been studied. XRD results confirmed that the hexaferrites with Nd-Zn content (x) of 0.00 ¡Â x ¡Â 0.24 were single M-type phase, and the hexaferrite with x = 0.30 exhibited the M-type phase and impurity phase. The remanence (B_r) increased with x from 0.00 to 0.06, and then decreased when x ¡Ã 0.06. The intrinsic coercivity (H_cj) and magnetic induction coercivity (H_cb) decreased with x from 0.00 to 0.30. B_r indicated a linear decreasing behavior with increasing temperature from 20 ^oC to 140 ^oC. H_cj raised linearly with increasing temperature from 20 ^oC to 140 ^oC. The value of a_Br basically remained constant with Nd-Zn content (x). The value of a_Hcj increased with x from 0.00 to 0.12, and began to decrease when x ¡Ã 0.12. The electrical resitivity (¥ñ) presented a decreasing trend with x from 0.00 to 0.30.

Keywords: M-type hexaferrites, Solid-state reaction route, X-ray diffraction, Magnetic measurements

Hexagonal ferrites have received considerable attention of researchers and engineers since the discovery of the ferrite in the 1950s. Although not as powerful as the newest NdFeB or SmCo₅ magnets, they still have a large market share in the market of magnetic materials, because of their perfect chemical stability, high Curie temperature, high performance-price ratio, and easy methods of production [1, 2]. In addition, M-type hexaferrites can be widely utilized as microwave devices, permanent magnetic materials, radar communication and microwave devices [3-5]. Many preparation techniques have been used to prepare the M-type hexaferrites such as hydrothermal method [6], three-step calcination method [7], co-precipitation method [8], standard solid-state reaction route [9], molten flux calcination method [10], sol-gel method [11], pulsed laser deposition method [12], and extrusion-based three-dimensional (3D) printing [13]. In the above-mentioned methods, the solid-state reaction route was used to fabricate the hexaferrites because of a few several profitable factors, for example controllable grain size, low manufacturing cost, simple technology and high productive.
In order to modify the intrinsic magnetic properties of M-type hexaferrites, the M-type hexaferrites been doped with rare-earth metals and transition metals, or the combination of these [14-36]. Singh et al. reported the rare-earth substitution (La³⁺, Nd³⁺ and Sm³⁺ ) doped strontium ferrite (Sr-M), and the results exhibited that the magnetization moment (M_s) and remenance (M_r) decrease with increasing rare-earth ions substitution, while the enhancement of H_c values may be due to higher magnetocrystalline anisotropy [15]. The Nd-substituted strontium hexaferrites prepared by hydrothermal synthesis have been reported by Wang et al. [17], and it is found that Nd substitution with a Nd-Sr ratio of 1/8 enhances the coercivity without causing any significant deterioration in either the saturation magnetization or the remanence. Shekhawat et al. synthesized the La-Sm substituted Sr-hexaferrite SrAl₄(La_0.5Sm_0.5)_xFe_8-xO₁₉ (0.0 ≤ x ≤ 1.5) nanomaterials by the auto combustion method and found that the remanence magnetization increases while intrinsic coercivity decreases with substitution [18]. The Zn-doped Ba hexaferrite single crystals have been synthesized, and it is found that Zn substitution significantly influences the coercivity and magnetization of Ba hexaferrite while the Curie temperature was nearly constant over the range of doping [23]. Zhang et al. reported the Nd-Co doped strontium hexaferrites Sr_1-xNd_xFe_12-xCo_xO₁₉ (0.0 ≤ x ≤ 0.4) fabricated by sol-gel autocombustion method, and the results showed that Nd-Co substitution can improve the saturation magnetization and coercivity and reaches a maximum at x=0.2 [33]. Liu et al. prepared the Ce-Zn co-substituted M-type strontium hexaferrites by the ceramic method, and the results showed that M_s and H_c can be improved significantly [36].
In this article, in order to enhance the magnetic properties, we have selected a combination of Nd³⁺ and Zn²⁺ ions to substitute in the M-type Ba-Sr hexaferrites. The hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ (0.00 ¡Â x ¡Â 0.30) were successfully synthesized by the solid-state reaction route. Impact of Nd-Zn co-doping on the microstructural, spectral and electric properties was analyzed. Subsequently, the magnetic properties of hexaferrites with different Nd-Zn content (x) were systematically investigated under different temperatures from room temperature (20 ^oC) to 140 ^oC. The novelty of this work is doing a study on the temperature coefficient of remanence (B_r) (a_Br), and temperature coefficient of intrinsic coercivity (H_cj) (a_Hcj) for the Nd-Zn co-doped hexaferrites.

The hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ (0.00 ≤ x ≤ 0.30) were prepared via the solid-state reaction route [37]. Barium carbonate (BaCO₃), strontium carbonate (SrCO₃), metallic oxides (Nd₂O₃, Fe₂O₃ and ZnO) were weighted in stoichimetric ratio. And then, the raw materials were thoroughly mixed together in water for 10 h in a ball mill in order to obtain finely mixed powder. Further, the as-mixed powder was dried, and pressed into circular pellets with Φ30 × 16 mm. Subsequently, the pellets were calcined in a muffle furnace at 1,260 ^oC for 2.0 h. The calcined pellets were shattered in a vibration mill, and suitable additives (CaCO₃ 0.8 wt%, SiO₂ 0.2 wt% and Al₂O₃ 0.2 wt%) were added, then the mixture was wet-milled in a ball-mill for 16 h. This procedure guarantees a narrow particle size distribution with the mean size of around 0.75 μm. The fine milled hexaferrite slurry was pressed into circular pellets with Φ30 × 16 mm in a magnetic field of 1.2 T. In order to measure the DC electrical resitivity, the fine milled hexaferrite slurry was dried, and then pressed into circular pellets with Φ20 × 8 mm. Finally, all green pellets were sintered in a muffle furnace at 1,185 ^oC for 1.5 h.
The phase identification and structural characterization of synthesized samples were performed by X-ray diffraction (XRD, Rigaku Smartlab). The surface morphology of the hexaferrites was detected by a field emission scanning electron microscopy (FE-SEM, HITACHI S-4800). The magnetic properties were measured at different temperatures from room temperature (20 ^oC) to 140 ^oC using a Hysteresis graph meter (NIM-2000HF, National Institute of Metrology of China). (Resistivity testing system, Ningbo rooko FT-353) was used to measure the DC electrical resitivity (ρ) of the hexaferrites at room temperature.

Fig. 1 presents the XRD patterns of hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ with different Nd-Zn content (x). The characteristics peaks were compared with the M-type hexaferrite ICCD card No. 51-1879. It can be observed that the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-x     Zn_xO₁₉ with Nd-Zn content (x) ≤ 0.24 belonged to M-type hexagonal crystal structure. The presence of hematite (α-Fe₂O₃) (ICCD card no. 89-0599) detected for the hexaferrite with Nd-Zn content (x) = 0.30 might be due the incomplete reaction under the preparing conditions. These show that the maximum doped content of Nd-Zn co-doping can not exceed x = 0.24.
The lattice parameters c and a of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ were calculated using to the following formula [38].
 
 

 
 
In the given relation, d_hkl is the interplaner spacing of the lines in XRD pattern and h, k and l are the Miller indices. The values of lattice parameters c and a for the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ with different Nd-Zn content (x) are listed in Table 1. The values of c and a decrease with increasing Nd-Zn content (x) from 0.00 to 0.30. The possible explanation for the decrease of c and a with increasing Nd-Zn content (x) can be attributed to the difference in the ionic radii (Δr) of the metal ions and the number of ionic substitutions of each species. Substitution of Sr²⁺ (r = 1.180 Å) by Nd³⁺ (r = 0.983 Å) makes a negative difference in the ionic radii of Δr = -0.197 Å. Substitution of Fe³⁺ (r = 0.645 Å) by Zn²⁺ (r = 0. 740 Å) makes a positive difference in the ionic radii of Δr = +0.095 Å. As in the case of Nd-Zn content (x) = 0.12, the lattice parameter c and a are decreased.
The unit cell volume (V_cell) of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ was calculated from the following equation [38]:
 
 

 
And its values are summarized in Table 1. It is clearly seen that the unit cell volume (V_cell) decreases with Nd-Zn content (x) from 0.00 to 0.30. The decrease in the V_cell is due to the decrease of lattice parameters c and a with increasing Nd-Zn content (x) as shown in Table 1. The X-ray density (d_xrd) has been calculated by using the below formula [39]:
 
 

 
 
where Z is the number of molecular per unit cell, M is the molecular weight, N_A is Avogadro’s number and V_cell is unit cell volume. And the values d_xrd are listed in Table 1. It noticed that the value of d_X-ray enhances from 5.194 g/cm³ at x = 0.00 to 5.321 g/cm³ at x = 0.30. The enhancement of d_xrd with increasing Nd-Zn content (x) can be attributed to the larger molecular weight and decreasing trend of unit cell volume (V_cell) for the Nd-Zn co-doped hexaferrites displayed in Table 1.
Fig. 2 shows the FE-SEM images of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ with x = 0.00, x = 0.12, and x = 0.24. This indicates that the grains in the hexaferrites are homogeneous distribution with hexagonal plate like shape. The average grain size increases from 1.8 μm at x = 0.00 to 3.2 μm at x = 0.24.
Fig. 3 represents the room temperature demagnetizing curves of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ with different Nd-Zn content (x). As revealed by the demagnetizing curves, the magnetic properties of the hexaferrites are greatly influenced by the substitution of Sr²⁺ ion by Nd³⁺ ion and Fe³⁺ ion by Zn²⁺ ion. The remanence (B_r), magnetic induction coercivity (H_cb), and intrinsic coercivity (H_cj) at the room temperature are derived from the demagnetizing curves of the hexaferrites samples with different Nd-Zn content (x).
The remanence (B_r) of the hexaferrites Ba_0.40Sr_0.60-x                  Nd_xFe_12.00-xZn_xO₁₉ as a function of Nd-Zn content (x) is plotted in Fig. 4(a). It is clearer that a suitable amount of Nd-Zn substitution can increase the remanence (B_r) of the hexaferrites. In Fig. 4(a), with increasing Nd-Zn content (x), B_r first increases and reaches to the maximum value of 386.0 mT at Nd-Zn content (x) = 0.06, and then decreases when Nd-Zn content (x) ≥ 0.06. The changing trend of remanence (B_r) can be explained on the basis of the occupation of the substituted ions and the impurity phase. M-type hexaferrites belong to P6₃/mmc space group, and have five crystallographic sublattices, such as three kinds of octahedral sites (2a, 12k, 4f₂), one tetrahedral site (4f₁) and one bipyramidal site (2b). The 2a, 12k and 2b sites have upward spin direction, and the 4f₁ and 4f₂ sites have downward spin direction [37, 40]. Herme et al. [41] have reported that in the M-type hexaferrites, Nd³⁺ ions substitute the Sr²⁺ sites in the vicinity of 4f₂ sites via Mössbauer analysis. Lee et al. [42] have reported that Zn²⁺ ions prefer to occupy the 4f₁ and 2b sites of tetrahedral sites in the M-type hexagonal structure by Mössbauer spectra. Zn²⁺ ion is nonmagnetic. And the magnetic moment of Fe³⁺ ion is 5 μ_B. Therefore, the increase of remanence (B_r) for the hexaferrites with increasing Nd-Zn content (x) from 0.00 to 0.06 is probably due to the below factor. When Nd-Zn content (x) ≤ 0.06, the number of Zn²⁺ ions entering 4f₁ sites (spin down) is more than that of Zn²⁺ ions entering 2b sites (spin up). This in turn decreases the negative magnetic moment of Fe³⁺ ions. Consequently, according to equation (3), the whole magnetic moment is enhanced. This leads to the increase of the remanence (B_r). When Nd-Zn content (x) ≥ 0.06, the decrease of remanence (B_r) for the hexaferrites may be attributed to the below three reasons. Firstly, at Nd-Zn content (x) ≥ 0.06, Zn²⁺ ions substitute Fe³⁺ ions in 2b sites having spin-up. According to equation (3), this in turn decreases the whole magnetic moment. This results in the decrease of the remanence (B_r). Secondly, Zn²⁺ (0 μ_B) ions substituting magnetic Fe³⁺ ions (5 μ_B) weaken the super-exchange interaction between metallic ions in the M-type hexaferrites, and then the remanence (B_r) is decreased. Thirdly, when Nd-Zn content (x) = 0.30, as seen from Fig. 1, the impurity phase (hematite: α-Fe₂O₃) leads to the decrease of remanence (B_r).
Fig. 4(b) shows the intrinsic coercivity (H_cj) and magnetic induction coercivity (H_cb) of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ as a function of Nd-Zn content (x). As shown in Fig. 4(b), the values of H_cj and H_cb show a decreasing trend with increasing Nd-Zn content (x), and decrease from 225.0 and 215.9 kA/m at x = 0.00 to 126.2 and 120.7 kA/m at x = 0.30, respectively. This proposes that Nd-Zn co-substitution can modify the coercivity of M-type Ba-Sr hexaferrites. Yang et al. [43] have reported that in the M-type hexaferrites, the ions at octahedral 4f₂ site and bipyramidal 2b site are known to be the main contributors to the magnetocrystalline anisotropy. According to the Stroner-Wohlfarth theory, the intrinsic coercivity (H_cj) of the M-type hexaferrites which results from coherent rotation of magnetization can be calculated by the following equation [44]:
 
 

 
where C is dimensionless constant of material, K₁ is the first anisotropy constant, and N is the grain demagnetization factor. Therefore, according to the equation (4), the decrease of H_cj with increasing Nd-Zn content (x) from 0.00 to 0.30 could be due to the following two reasons. Firstly, as seen from Fig. 2, the average grain size of M-type hexaferrite increases with increasing Nd-Zn content (x) from 0.00 to 0.30. Thus, the value of N increases with increasing Nd-Zn content (x). According to equation (4), the value of H_cj is decreased. Secondly, the results of Mössbauer spectra showed that Zn²⁺ ions prefer to occupy the 4f₁ and 2b sites of tetrahedral sites in the M-type hexagonal structure [42]. The decrease of H_cj with increasing Nd-Zn content (x) may be related to the reduction of magnetocrystalline anisotropy field as a result of Zn²⁺ substitution for Fe³⁺ ions at 2b sites.
The temperature dependent demagnetizing curves of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ with different Nd-Zn content (x) are presented in Fig. 5. The changing trend of the demagnetizing curves measured at different temperatures is in agreement with that reported by T.D.K. Corporation [45] and A. Goldman et al. [46]. The values of the remanence (B_r), and intrinsic coercivity (H_cj) at different temperatures are calculated from the demagnetizing curves for the hexaferrites with different Nd-Zn content (x). Fig. 6(a) presents the temperature dependent remanence (B_r) between 20 ^oC and 140 ^oC for the hexaferrites with different Nd-Zn content (x). As seen from Fig. 6(a), for the hexaferrites with different Nd-Zn content (x), the values of remanence (B_r) have a linear decreasing behavior with increasing temperature from 20 ^oC to 140 ^oC. This is in agreement with the results reported by Zhou et al. [47]. The variations of the intrinsic coercivity (H_cj) between 20 ^oC and 140 ^oC for the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ with different Nd-Zn content (x) are shown in Fig. 6(b). It is observed that for the hexaferrites with different Nd-Zn content (x), the values of intrinsic coercivity (H_cj) raise linearly with increasing temperature from 20 ^oC to 140 ^oC. This agrees with the changing trend reported by W. Zhou [48] and T.D.K. Corporation [49].
When the ambient temperature ¡Â 400 ^oC, the remanence (B_r) of hexaferrites BaFe₁₂O₁₉ deareases linearly with increasing temperature [50]. The temperature coefficient of remanence (B_r) can be approximated as a constant in a certain temperature range. Therefore, the average temperature coefficient of B_r (a_Br) of hexaferrites can be defined as the below relation [48]:
 

 
where B_r(20) is the value of remanence (B_r) measured at 20 ^oC, B_r(t) is the value of remanence (B_r) measured at temperature of t ^oC. Fig. 7(a) represents the variation of a_Br of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ as a function of Nd-Zn content (x). It is clear from Fig. 7(a) that the value of a_Br basically remains constant around -0.175 %/^oC. The value of a_Br is in agreement with that reported by T.D.K. Corporation [45]. This indicates that the Nd-Zn substitution have not big impact on the average temperature coefficient of remanence (B_r) (a_Br) of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉.
As shown in Fig. 6(b), the values of intrinsic coercivity (H_cj) have a linear behavior with temperature from 20 ^oC to 140 ^oC. The temperature coefficient of intrinsic coercivity (H_cj) is also approximated as a constant in a certain temperature range [49]. Thus, the average temperature coefficient of H_cj (a_Hcj) can be calculated using the following equation [43]:
 

 
where H_cj(20) is the value of intrinsic coercivity (H_cj) measured at 20 ^oC, H_cj(t) is the value of intrinsic coercivity (H_cj) measured at temperature of t ^oC. The influence of Nd-Zn content (x) on the average temperature coefficient of intrinsic coercivity (H_cj) (a_Hcj) of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ is plotted in Fig. 7(b). It is noted that the value of a_Hcj firstly increases from 0.417 %/^oC at x=0.00 to 0.573 %/^oC at x = 0.12, and then decreases when Nd-Zn content (x) ¡Ã 0.12. This shows that Nd-Zn content (x) can significantly affect the values of a_Hcj. The values of a_Hcj are larger than that reported by T.D.K. Corporation [49], which should the values of intrinsic coercivity (H_cj) in this study are lower than that in TDK Products Catalog [49].
Fig. 8 illustrates the impact of Nd-Zn content (x) on the DC electrical resistivity (ρ) of the hexaferrites Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉. It is clear that the electrical resistivity (ρ) is strongly affected by Nd-Zn content (x). It is observed that the value of electrical resitivity (ρ) decreases from 679.9 × 10⁷ Ω-Cm at x = 0.00 to 0.13 × 10⁷ Ω-Cm at x = 0.30. The mechanism of conductivity in the hexaferrites is attributed to the hopping of electrons between Fe³⁺ and Fe²⁺ ions at the octahedral sites [50]. Van Diepen et al. have reported that the substitution of La³⁺ for Ba²⁺ or Sr²⁺ in M-type ferrites is associated with a valence change of Fe³⁺ to Fe²⁺ at 2a or 4f₂ site [51]. Thus, as Nd³⁺ ions substitute Sr²⁺ ions and Zn²⁺ ions substitute Fe³⁺ ions, some Fe³⁺ ions will change into Fe²⁺ ions. This increases the number of Fe²⁺ ions which leads to the increase of the hopping probability between the Fe³⁺ and Fe²⁺ ions. Thus, the above reasons result in the decrease of electrical resitivity (ρ).

The solid-state reaction route was used to synthesize the Nd-Zn substituted M-type hexaferrites with nominal compositions Ba_0.40Sr_0.60-xNd_xFe_12.00-xZn_xO₁₉ (0.00 ¡Â x ¡Â 0.30). The X-ray diffraction patterns show that the hexaferrites with Nd-Zn content (x) of 0.00 ¡Â x ¡Â 0.24 were single M-type phase, while the hexaferrites with Nd-Zn content (x) = 0.30 exhibited the M-type phase and impurity phases. FE-SEM images proposed that all the particles were regular hexagonal platelet-like shape and the average particle size increased with increasing Nd-Zn content (x). B_r increased with Nd-Zn content (x) from 0.00 to 0.06, and then started to decrease when Nd-Zn content (x) ¡Ã 0.06. H_cj and H_cb decreased with Nd-Zn content (x) from 0.00 to 0.30. B_r indicated a linear decreasing behavior with increasing temperature from 20 ^oC to 140 ^oC. H_cj raise linearly with increasing temperature from 20 ^oC to 140 ^oC. The value of a_Br basically remained constant with Nd-Zn content (x). The value of a_Hcj firstly increased with x from 0.00 to 0.12, and then decreased when x ¡Ã 0.12. The electrical resitivity (¥ñ) presented a decreasing trend with x from 0.00 to 0.30.

This work was supported by the National Natural Science Foundation of China (Nos. 51872004, 51802002), Education Department of Anhui Province (Nos. KJ2013B293, KJ2018A0039), Key Program of the Science and Technology of Anhui Province (Grant No. S201904a09020074).